- FindStat

Identifier

Mp00027: Dyck paths —to partition⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
St001195: Dyck paths ⟶ ℤ

Values

[1,0,1,0,1,0,1,0] => [3,2,1] => [2,1] => [1,0,1,1,0,0] => 1

[1,0,1,0,1,1,0,0] => [2,2,1] => [2,1] => [1,0,1,1,0,0] => 1

[1,0,1,0,1,0,1,0,1,0] => [4,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 1

[1,0,1,0,1,0,1,1,0,0] => [3,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 1

[1,0,1,0,1,1,0,0,1,0] => [4,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 1

[1,0,1,0,1,1,0,1,0,0] => [3,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 1

[1,0,1,0,1,1,1,0,0,0] => [2,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 1

[1,0,1,1,0,0,1,0,1,0] => [4,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 1

[1,0,1,1,0,0,1,1,0,0] => [3,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 1

[1,0,1,1,0,1,0,0,1,0] => [4,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1

[1,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1

[1,0,1,1,0,1,1,0,0,0] => [2,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1

[1,0,1,1,1,0,0,0,1,0] => [4,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 1

[1,0,1,1,1,0,0,1,0,0] => [3,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 1

[1,0,1,1,1,0,1,0,0,0] => [2,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 1

[1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 1

[1,1,0,0,1,0,1,0,1,0] => [4,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => 1

[1,1,0,0,1,0,1,1,0,0] => [3,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => 1

[1,1,0,0,1,1,0,0,1,0] => [4,2,2] => [2,2] => [1,1,1,0,0,0] => 1

[1,1,0,0,1,1,0,1,0,0] => [3,2,2] => [2,2] => [1,1,1,0,0,0] => 1

[1,1,0,0,1,1,1,0,0,0] => [2,2,2] => [2,2] => [1,1,1,0,0,0] => 1

[1,1,0,1,0,0,1,0,1,0] => [4,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 1

[1,1,0,1,0,0,1,1,0,0] => [3,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 1

[1,1,0,1,0,1,0,0,1,0] => [4,2,1] => [2,1] => [1,0,1,1,0,0] => 1

[1,1,0,1,0,1,0,1,0,0] => [3,2,1] => [2,1] => [1,0,1,1,0,0] => 1

[1,1,0,1,0,1,1,0,0,0] => [2,2,1] => [2,1] => [1,0,1,1,0,0] => 1

[1,1,1,0,0,0,1,0,1,0] => [4,3] => [3] => [1,0,1,0,1,0] => 0

[1,1,1,0,0,0,1,1,0,0] => [3,3] => [3] => [1,0,1,0,1,0] => 0

[1,0,1,0,1,1,1,0,0,0,1,0] => [5,2,2,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 1

[1,0,1,0,1,1,1,0,0,1,0,0] => [4,2,2,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 1

[1,0,1,0,1,1,1,0,1,0,0,0] => [3,2,2,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 1

[1,0,1,0,1,1,1,1,0,0,0,0] => [2,2,2,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 1

[1,0,1,1,0,1,1,0,0,0,1,0] => [5,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 1

[1,0,1,1,0,1,1,0,0,1,0,0] => [4,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 1

[1,0,1,1,0,1,1,0,1,0,0,0] => [3,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 1

[1,0,1,1,0,1,1,1,0,0,0,0] => [2,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 1

[1,0,1,1,1,0,1,0,0,0,1,0] => [5,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 1

[1,0,1,1,1,0,1,0,0,1,0,0] => [4,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 1

[1,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 1

[1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 1

[1,0,1,1,1,1,0,0,0,0,1,0] => [5,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 1

[1,0,1,1,1,1,0,0,0,1,0,0] => [4,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 1

[1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 1

[1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 1

[1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 1

[1,1,0,0,1,0,1,1,0,0,1,0] => [5,3,3,2] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 1

[1,1,0,0,1,0,1,1,0,1,0,0] => [4,3,3,2] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 1

[1,1,0,0,1,0,1,1,1,0,0,0] => [3,3,3,2] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 1

[1,1,0,0,1,1,0,1,0,0,1,0] => [5,3,2,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 1

[1,1,0,0,1,1,0,1,0,1,0,0] => [4,3,2,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 1

[1,1,0,0,1,1,0,1,1,0,0,0] => [3,3,2,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 1

[1,1,0,0,1,1,1,0,0,0,1,0] => [5,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => 1

[1,1,0,0,1,1,1,0,0,1,0,0] => [4,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => 1

[1,1,0,0,1,1,1,0,1,0,0,0] => [3,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => 1

[1,1,0,0,1,1,1,1,0,0,0,0] => [2,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => 1

[1,1,0,1,0,0,1,1,0,0,1,0] => [5,3,3,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 1

[1,1,0,1,0,0,1,1,0,1,0,0] => [4,3,3,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 1

[1,1,0,1,0,0,1,1,1,0,0,0] => [3,3,3,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 1

[1,1,0,1,0,1,0,1,0,0,1,0] => [5,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 1

[1,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 1

[1,1,0,1,0,1,0,1,1,0,0,0] => [3,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 1

[1,1,0,1,0,1,1,0,0,0,1,0] => [5,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 1

[1,1,0,1,0,1,1,0,0,1,0,0] => [4,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 1

[1,1,0,1,0,1,1,0,1,0,0,0] => [3,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 1

[1,1,0,1,0,1,1,1,0,0,0,0] => [2,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 1

[1,1,0,1,1,0,0,1,0,0,1,0] => [5,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 1

[1,1,0,1,1,0,0,1,0,1,0,0] => [4,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 1

[1,1,0,1,1,0,0,1,1,0,0,0] => [3,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 1

[1,1,0,1,1,0,1,0,0,0,1,0] => [5,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1

[1,1,0,1,1,0,1,0,0,1,0,0] => [4,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1

[1,1,0,1,1,0,1,0,1,0,0,0] => [3,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1

[1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1

[1,1,0,1,1,1,0,0,0,0,1,0] => [5,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 1

[1,1,0,1,1,1,0,0,0,1,0,0] => [4,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 1

[1,1,0,1,1,1,0,0,1,0,0,0] => [3,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 1

[1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 1

[1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 1

[1,1,1,0,0,0,1,0,1,0,1,0] => [5,4,3] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 1

[1,1,1,0,0,0,1,0,1,1,0,0] => [4,4,3] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 1

[1,1,1,0,0,0,1,1,0,0,1,0] => [5,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => 1

[1,1,1,0,0,0,1,1,0,1,0,0] => [4,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => 1

[1,1,1,0,0,0,1,1,1,0,0,0] => [3,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => 1

[1,1,1,0,0,1,0,0,1,0,1,0] => [5,4,2] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 1

[1,1,1,0,0,1,0,0,1,1,0,0] => [4,4,2] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 1

[1,1,1,0,0,1,0,1,0,0,1,0] => [5,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => 1

[1,1,1,0,0,1,0,1,0,1,0,0] => [4,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => 1

[1,1,1,0,0,1,0,1,1,0,0,0] => [3,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => 1

[1,1,1,0,0,1,1,0,0,0,1,0] => [5,2,2] => [2,2] => [1,1,1,0,0,0] => 1

[1,1,1,0,0,1,1,0,0,1,0,0] => [4,2,2] => [2,2] => [1,1,1,0,0,0] => 1

[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,2] => [2,2] => [1,1,1,0,0,0] => 1

[1,1,1,0,0,1,1,1,0,0,0,0] => [2,2,2] => [2,2] => [1,1,1,0,0,0] => 1

[1,1,1,0,1,0,0,0,1,0,1,0] => [5,4,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 1

[1,1,1,0,1,0,0,0,1,1,0,0] => [4,4,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 1

[1,1,1,0,1,0,0,1,0,0,1,0] => [5,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 1

[1,1,1,0,1,0,0,1,0,1,0,0] => [4,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 1

[1,1,1,0,1,0,0,1,1,0,0,0] => [3,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 1

[1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,1] => [2,1] => [1,0,1,1,0,0] => 1

[1,1,1,0,1,0,1,0,0,1,0,0] => [4,2,1] => [2,1] => [1,0,1,1,0,0] => 1

[1,1,1,0,1,0,1,0,1,0,0,0] => [3,2,1] => [2,1] => [1,0,1,1,0,0] => 1

[1,1,1,0,1,0,1,1,0,0,0,0] => [2,2,1] => [2,1] => [1,0,1,1,0,0] => 1

[1,1,1,1,0,0,0,0,1,0,1,0] => [5,4] => [4] => [1,0,1,0,1,0,1,0] => 0

>>> Load all 533 entries. <<<

[1,1,1,1,0,0,0,0,1,1,0,0] => [4,4] => [4] => [1,0,1,0,1,0,1,0] => 0

[1,1,1,1,0,0,0,1,0,0,1,0] => [5,3] => [3] => [1,0,1,0,1,0] => 0

[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3] => [3] => [1,0,1,0,1,0] => 0

[1,1,1,1,0,0,0,1,1,0,0,0] => [3,3] => [3] => [1,0,1,0,1,0] => 0

[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 1

[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 1

[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 1

[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 1

[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 1

[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 1

[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 1

[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [5,2,2,2,2] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 1

[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [4,2,2,2,2] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 1

[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 1

[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 1

[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 1

[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 1

[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 1

[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 1

[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 1

[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 1

[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 1

[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 1

[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 1

[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 1

[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 1

[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 1

[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 1

[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 1

[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 1

[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 1

[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 1

[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 1

[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 1

[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 1

[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 1

[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => 1

[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => 1

[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => 1

[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => 1

[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [6,3,3,2] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 1

[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 1

[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 1

[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 1

[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [6,3,2,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 1

[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 1

[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 1

[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 1

[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => 1

[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => 1

[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => 1

[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => 1

[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => 1

[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [6,3,3,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 1

[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 1

[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 1

[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 1

[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 1

[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 1

[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 1

[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 1

[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 1

[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 1

[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 1

[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 1

[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 1

[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 1

[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 1

[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 1

[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 1

[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1

[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1

[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1

[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1

[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1

[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 1

[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 1

[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 1

[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 1

[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 1

[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 1

[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [6,4,4] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => 1

[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [5,4,4] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => 1

[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,4,4] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => 1

[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [6,4,3] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 1

[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [5,4,3] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 1

[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,4,3] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 1

[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [6,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => 1

[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [5,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => 1

[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => 1

[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [3,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => 1

[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [6,4,2] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 1

[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [5,4,2] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 1

[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,4,2] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 1

[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [6,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => 1

[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [5,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => 1

[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => 1

[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [3,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => 1

[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,2,2] => [2,2] => [1,1,1,0,0,0] => 1

[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [5,2,2] => [2,2] => [1,1,1,0,0,0] => 1

[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,2,2] => [2,2] => [1,1,1,0,0,0] => 1

[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [3,2,2] => [2,2] => [1,1,1,0,0,0] => 1

[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,2,2] => [2,2] => [1,1,1,0,0,0] => 1

[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [6,4,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 1

[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,4,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 1

[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,4,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 1

[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 1

[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [5,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 1

[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 1

[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [3,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 1

[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,2,1] => [2,1] => [1,0,1,1,0,0] => 1

[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [5,2,1] => [2,1] => [1,0,1,1,0,0] => 1

[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,2,1] => [2,1] => [1,0,1,1,0,0] => 1

[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1] => [2,1] => [1,0,1,1,0,0] => 1

[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,2,1] => [2,1] => [1,0,1,1,0,0] => 1

[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,5] => [5] => [1,0,1,0,1,0,1,0,1,0] => 0

[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => [5] => [1,0,1,0,1,0,1,0,1,0] => 0

[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [6,4] => [4] => [1,0,1,0,1,0,1,0] => 0

[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4] => [4] => [1,0,1,0,1,0,1,0] => 0

[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [4,4] => [4] => [1,0,1,0,1,0,1,0] => 0

[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,3] => [3] => [1,0,1,0,1,0] => 0

[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,3] => [3] => [1,0,1,0,1,0] => 0

[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [4,3] => [3] => [1,0,1,0,1,0] => 0

[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [3,3] => [3] => [1,0,1,0,1,0] => 0

[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 1

[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 1

[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 1

[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 1

[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 1

[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 1

[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 1

[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 1

[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 1

[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 1

[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 1

[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 1

[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 1

[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 1

[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 1

[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 1

[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 1

[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 1

[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 1

[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 1

[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 1

[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 1

[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 1

[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 1

[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 1

[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 1

[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 1

[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 1

[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 1

[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 1

[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 1

[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 1

[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 1

[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 1

[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 1

[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 1

[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 1

[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 1

[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [7,3,3,3] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => 1

[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => 1

[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => 1

[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => 1

[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => 1

[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [7,3,3,2] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 1

[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 1

[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 1

[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 1

[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 1

[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 1

[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 1

[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 1

[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 1

[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 1

[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => 1

[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => 1

[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => 1

[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => 1

[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => 1

[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => 1

[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [7,3,3,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 1

[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 1

[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 1

[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 1

[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 1

[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 1

[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 1

[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 1

[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 1

[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 1

[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 1

[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 1

[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 1

[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 1

[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 1

[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 1

[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 1

[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 1

[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 1

[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 1

[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 1

[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1

[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1

[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1

[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1

[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1

[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1

[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 1

[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 1

[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 1

[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 1

[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 1

[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 1

[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 1

[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [7,4,4] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => 1

[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [6,4,4] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => 1

[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,4,4] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => 1

[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [4,4,4] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => 1

[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [7,4,3] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 1

[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [6,4,3] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 1

[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [5,4,3] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 1

[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [4,4,3] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 1

[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [7,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => 1

[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [6,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => 1

[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [5,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => 1

[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [4,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => 1

[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [3,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => 1

[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [7,4,2] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 1

[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [6,4,2] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 1

[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [5,4,2] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 1

[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [4,4,2] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 1

[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [7,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => 1

[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [6,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => 1

[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => 1

[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [4,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => 1

[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [3,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => 1

[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [7,2,2] => [2,2] => [1,1,1,0,0,0] => 1

[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [6,2,2] => [2,2] => [1,1,1,0,0,0] => 1

[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [5,2,2] => [2,2] => [1,1,1,0,0,0] => 1

[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [4,2,2] => [2,2] => [1,1,1,0,0,0] => 1

[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [3,2,2] => [2,2] => [1,1,1,0,0,0] => 1

[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [2,2,2] => [2,2] => [1,1,1,0,0,0] => 1

[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [7,4,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 1

[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [6,4,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 1

[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [5,4,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 1

[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [4,4,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 1

[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [7,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 1

[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [6,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 1

[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [5,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 1

[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [4,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 1

[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [3,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 1

[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [7,2,1] => [2,1] => [1,0,1,1,0,0] => 1

[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [6,2,1] => [2,1] => [1,0,1,1,0,0] => 1

[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [5,2,1] => [2,1] => [1,0,1,1,0,0] => 1

[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [4,2,1] => [2,1] => [1,0,1,1,0,0] => 1

[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [3,2,1] => [2,1] => [1,0,1,1,0,0] => 1

[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [2,2,1] => [2,1] => [1,0,1,1,0,0] => 1

[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [7,5] => [5] => [1,0,1,0,1,0,1,0,1,0] => 0

[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5] => [5] => [1,0,1,0,1,0,1,0,1,0] => 0

[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [5,5] => [5] => [1,0,1,0,1,0,1,0,1,0] => 0

[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [7,4] => [4] => [1,0,1,0,1,0,1,0] => 0

[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [6,4] => [4] => [1,0,1,0,1,0,1,0] => 0

[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [5,4] => [4] => [1,0,1,0,1,0,1,0] => 0

[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [4,4] => [4] => [1,0,1,0,1,0,1,0] => 0

[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,3] => [3] => [1,0,1,0,1,0] => 0

[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,3] => [3] => [1,0,1,0,1,0] => 0

[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [5,3] => [3] => [1,0,1,0,1,0] => 0

[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [4,3] => [3] => [1,0,1,0,1,0] => 0

[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [3,3] => [3] => [1,0,1,0,1,0] => 0

[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0] => [8,3] => [3] => [1,0,1,0,1,0] => 0

[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0] => [8,2,1] => [2,1] => [1,0,1,1,0,0] => 1

[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 1

[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0] => [9,3] => [3] => [1,0,1,0,1,0] => 0

[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0] => [9,2,1] => [2,1] => [1,0,1,1,0,0] => 1

[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 1

[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0] => [8,4] => [4] => [1,0,1,0,1,0,1,0] => 0

[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0] => [8,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 1

[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => [8,2,2] => [2,2] => [1,1,1,0,0,0] => 1

[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0] => [8,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1

[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 1

[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,1,0] => [10,2,1] => [2,1] => [1,0,1,1,0,0] => 1

[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,1,0] => [9,4] => [4] => [1,0,1,0,1,0,1,0] => 0

[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,1,0] => [9,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 1

[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,1,0] => [9,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1

[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 1

[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0] => [8,5] => [5] => [1,0,1,0,1,0,1,0,1,0] => 0

[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,1,0] => [8,4,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 1

[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0] => [8,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => 1

[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0] => [8,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 1

[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,1,0] => [8,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 1

[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,1,0] => [8,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 1

[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 1

[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0] => [9,5] => [5] => [1,0,1,0,1,0,1,0,1,0] => 0

[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,1,0] => [9,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => 1

[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,1,0] => [9,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 1

[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 1

[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,1,0] => [8,4,2] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 1

[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,1,0] => [8,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => 1

[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => [8,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 1

[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,0] => [8,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 1

[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,1,0] => [9,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => 1

[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0] => [9,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 1

[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,1,0] => [9,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => 1

[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,1,0] => [8,3,3,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 1

[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,1,0] => [8,3,2,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 1

[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,1,0] => [8,3,3,3] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => 1

[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 1

[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 1

[1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 1

[1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 1

[1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 1

[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 1

[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 1

[1,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,2,2,2] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 1

[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,2,2,2] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 1

[1,1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,2] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 1

[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 1

[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0,0] => [7,2,2,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 1

[1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 1

[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 1

[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 1

[1,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 1

[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 1

[1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 1

[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 1

[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 1

[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 1

[1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 1

[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 1

[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 1

[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 1

[1,1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0,0] => [4,3,3,3] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => 1

[1,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0] => [6,3,3,2] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 1

[1,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0] => [3,3,2,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 1

[1,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0,0] => [5,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => 1

[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,0] => [6,3,3,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 1

[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0] => [4,3,3,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 1

[1,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0,0] => [3,3,3,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 1

[1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0] => [6,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 1

[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 1

[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 1

[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 1

[1,1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0,0] => [4,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 1

[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 1

[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 1

[1,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 1

[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 1

[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1

[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1

[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1

[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 1

[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 1

[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 1

[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 1

[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 1

[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 1

[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 1

[1,1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0,0] => [5,4,4] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => 1

[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0] => [4,4,4] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => 1

[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 1

[1,1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0,0] => [4,4,3] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 1

[1,1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0,0] => [6,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => 1

[1,1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,0] => [4,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => 1

[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0] => [3,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => 1

[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0] => [6,4,2] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 1

[1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 1

[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,0] => [4,4,2] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 1

[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => 1

[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => 1

[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => 1

[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0,0] => [7,2,2] => [2,2] => [1,1,1,0,0,0] => 1

[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0] => [4,2,2] => [2,2] => [1,1,1,0,0,0] => 1

[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2] => [2,2] => [1,1,1,0,0,0] => 1

[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2] => [2,2] => [1,1,1,0,0,0] => 1

[1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 1

[1,1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0,0] => [4,4,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 1

[1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0] => [6,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 1

[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0] => [5,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 1

[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 1

[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 1

[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1] => [2,1] => [1,0,1,1,0,0] => 1

[1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,0] => [6,2,1] => [2,1] => [1,0,1,1,0,0] => 1

[1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1] => [2,1] => [1,0,1,1,0,0] => 1

[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1] => [2,1] => [1,0,1,1,0,0] => 1

[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1] => [2,1] => [1,0,1,1,0,0] => 1

[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1] => [2,1] => [1,0,1,1,0,0] => 1

[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0] => [7,5] => [5] => [1,0,1,0,1,0,1,0,1,0] => 0

[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0] => [5,5] => [5] => [1,0,1,0,1,0,1,0,1,0] => 0

[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0] => [4,4] => [4] => [1,0,1,0,1,0,1,0] => 0

[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0] => [7,3] => [3] => [1,0,1,0,1,0] => 0

[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0] => [4,3] => [3] => [1,0,1,0,1,0] => 0

[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [3,3] => [3] => [1,0,1,0,1,0] => 0

[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [2,2,1] => [2,1] => [1,0,1,1,0,0] => 1

[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 1

[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 1

[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 1

[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0] => [8,2,1] => [2,1] => [1,0,1,1,0,0] => 1

[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0] => [3,3] => [3] => [1,0,1,0,1,0] => 0

[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0] => [3,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => 1

[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0] => [4,4,4] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => 1

[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => 1

[1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 1

[1,1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 1

[1,1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [4,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 1

[1,1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [5,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 1

[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 1

[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1] => [2,1] => [1,0,1,1,0,0] => 1

[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0,0] => [7,2,1] => [2,1] => [1,0,1,1,0,0] => 1

[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0,0] => [8,2,1] => [2,1] => [1,0,1,1,0,0] => 1

[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [6,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 1

[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [7,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 1

[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 1

[1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0] => [5,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 1

[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0,0] => [6,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 1

[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,0] => [5,4,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 1

[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0] => [4,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 1

[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2] => [2,2] => [1,1,1,0,0,0] => 1

[1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 1

[1,1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 1

[1,1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0] => [3,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 1

[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0,0] => [8,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 1

[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0] => [2,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1

[1,1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1

[1,1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0] => [3,3] => [3] => [1,0,1,0,1,0] => 0

[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0] => [5,5] => [5] => [1,0,1,0,1,0,1,0,1,0] => 0

[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0] => [4,4] => [4] => [1,0,1,0,1,0,1,0] => 0

[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0] => [5,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 1

[1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 1

[1,1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0] => [3,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => 1

search for individual values

searching the database for the individual values of this statistic

Description

The global dimension of the algebra

$A/AfA$ of the corresponding Nakayama algebra

$A$ with minimal left faithful projective-injective module

$Af$ .

Map

parallelogram polyomino

Description

Return the Dyck path corresponding to the partition interpreted as a parallogram polyomino.
The Ferrers diagram of an integer partition can be interpreted as a parallogram polyomino, such that each part corresponds to a column.
This map returns the corresponding Dyck path.

Map

first row removal

Description

Removes the first entry of an integer partition

Map

to partition

Description

The cut-out partition of a Dyck path.
The partition

$\lambda$ associated to a Dyck path is defined to be the complementary partition inside the staircase partition

$(n-1,\ldots,2,1)$ when cutting out

$D$ considered as a path from

$(0,0)$ to

$(n,n)$ .
In other words,

$\lambda_{i}$ is the number of down-steps before the

$(n+1-i)$ -th up-step of

$D$ .
This map is a bijection between Dyck paths of size

$n$ and partitions inside the staircase partition

$(n-1,\ldots,2,1)$ .